Main Property of the Jacobi Integral for Gravity Assist Maneuvers in the Solar System

Abstract

In the context of the circular restricted three-body problem (RTBP), the search for the spacecraft’s asymptotic velocity $${{V}_{\infty }}$$ for gravity assist maneuvers (GMs) can be performed using the Jacobi integral $$J$$ and the main property of the Jacobi integral constant for GMs, $${\text{const}} = J \approx 3 - V_{\infty }^{2}.$$ It is shown in the paper that the standard cumbersome way of traditional derivation of this property that is used in modern astrodynamics can be significantly simplified.